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Logic Programming pair #487529277
details
property
value
status
complete
benchmark
times.pl
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
SGST06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.82379102707 seconds
cpu usage
4.075838237
max memory
2.9730816E8
stage attributes
key
value
output-size
10697
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.pl /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.pl # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Left Termination of the query pattern times(g,g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof [SOUND, 0 ms] (2) PiTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) PiDP (5) DependencyGraphProof [EQUIVALENT, 1 ms] (6) PiDP (7) UsableRulesProof [EQUIVALENT, 0 ms] (8) PiDP (9) PiDPToQDPProof [SOUND, 0 ms] (10) QDP (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Clauses: times(X, Y, Z) :- mult(X, Y, 0, Z). mult(0, Y, 0, 0). mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z). mult(X, Y, s(W), s(Z)) :- mult(X, Y, W, Z). Query: times(g,g,a) ---------------------------------------- (1) PrologToPiTRSProof (SOUND) We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: times_in_3: (b,b,f) mult_in_4: (b,b,b,f) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: times_in_gga(X, Y, Z) -> U1_gga(X, Y, Z, mult_in_ggga(X, Y, 0, Z)) mult_in_ggga(0, Y, 0, 0) -> mult_out_ggga(0, Y, 0, 0) mult_in_ggga(s(U), Y, 0, Z) -> U2_ggga(U, Y, Z, mult_in_ggga(U, Y, Y, Z)) mult_in_ggga(X, Y, s(W), s(Z)) -> U3_ggga(X, Y, W, Z, mult_in_ggga(X, Y, W, Z)) U3_ggga(X, Y, W, Z, mult_out_ggga(X, Y, W, Z)) -> mult_out_ggga(X, Y, s(W), s(Z)) U2_ggga(U, Y, Z, mult_out_ggga(U, Y, Y, Z)) -> mult_out_ggga(s(U), Y, 0, Z) U1_gga(X, Y, Z, mult_out_ggga(X, Y, 0, Z)) -> times_out_gga(X, Y, Z) The argument filtering Pi contains the following mapping: times_in_gga(x1, x2, x3) = times_in_gga(x1, x2) U1_gga(x1, x2, x3, x4) = U1_gga(x1, x2, x4) mult_in_ggga(x1, x2, x3, x4) = mult_in_ggga(x1, x2, x3) 0 = 0 mult_out_ggga(x1, x2, x3, x4) = mult_out_ggga(x1, x2, x3, x4) s(x1) = s(x1) U2_ggga(x1, x2, x3, x4) = U2_ggga(x1, x2, x4) U3_ggga(x1, x2, x3, x4, x5) = U3_ggga(x1, x2, x3, x5) times_out_gga(x1, x2, x3) = times_out_gga(x1, x2, x3) Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog ---------------------------------------- (2) Obligation: Pi-finite rewrite system: The TRS R consists of the following rules:
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